Congruences and External Direct Sum of LA-Modules

Abstract

In this paper we study a new algebraic structure namely left almost module (LA-module in short). We extend the notion of congruences to LA-modules which is defined in1 for semigroups. We show that every homomorphism defines a congruence relation on LA-modules and prove analogues of isomorphism theorems. We also define external direct sum of LA-modules and show that the internal direct sum of LA-submodules is isomorphic to the external direct sum of those LA-submodules.